Anya Katsevich, New York University

Photo of Anya Katsevich

A microgrid is a modern power grid technology that can operate in stand-alone mode and has the potential to be much more efficient than traditional grids. However, significant fluctuations and uncertainty make reliability a major bottleneck for the implementation of the technology.

In this project, we build a novel probabilistic framework for analysis of how and when a microgrid can fail. This is an essential first step in developing remedial action schemes, which will require on-line spatio-temporal monitoring of potential failures.

In the absence of fluctuations, a system will stay balanced according to the power flow equations. Fluctuations, which are significant in micro-grids on both consumption and production levels, will drive the system out of equilibrium. We develop a stochastic model and monitor the probability that the fluctuations violate safety constraints, which could cause a line or other equipment to overheat and malfunction.

Fluctuations leading to failures are rare and slow. Mathematically, our task becomes estimating the probability of escape out of the safe region and finding a way to sample these rare trajectories of the system that start from the safe region and then cross the reliability boundary in finite time. We represent the reliability boundary as a union of constraints and approximate the escape probability as a union of rare events, each corresponding to crossing a boundary (associated with, for example, the overheating of a particular power line). In the dynamic case, we analyze the distribution of the first crossing time of the reliability boundary, using the idea that the probability will concentrate around the most likely escape path.

Abstract Author(s): Anya Katsevich, Michael Chertkov, Yury Maximov